I don’t think so any institution/or site provided Free online beauty courses, but on the net many site provided video or short lesion on Basic makeup like youtube etc.

Here I am providing lesson name which come under Basic makeup course provided by site on the net for sample classes on free of cost:

Less 1 Introduction
Less 2 Preparing the skin
Less 3 Materials. Face
Less 4 Materials. Eyes.
Less 5 Materials. Lips
Less 6 Materials. Brushes
Less 7 The base
Less 8 The base
Less 9 The eye concealer
Less 10 Face powder
Less 11 Eye brows
Less 12 Eye shadows
Less 13 Eye shadows
Less 14 Eye shadows
Less 15 Eye liners.
Less 16 Mascara: eye lashes
Less 17 Blush
Less 18 Blush
Less 19 Lips makeup
Less 20 Lips
Less 21 Illuminating Face powder
Less 22 Sealing makeup